Hadamard Product: Element Wise Matrix Multiplication

1. Hadamard Product or Element Wise Matrix Multiplication between any number of Matrices can be done if all the Matrices have Same Number of Rows and Same Number of Columns. The Resultant Matrix also has the Same Number of Rows and Columns as the input Matrices.
2. Given 2 \(M \times N\) Matrices, Matrix \(A\) having elements \(a_{ij}\) and Matrix \(B\) having elements \(b_{ij}\) as following
   
   \(A=\begin{bmatrix} a_{11} & a_{12} & ... & a_{1n}\\ a_{21} & a_{22} & ... & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\a_{m1} & a_{m2} & ... & a_{mn}\end{bmatrix} \hspace{.5cm}B=\begin{bmatrix} b_{11} & b_{12} & ... & b_{1n}\\ b_{21} & b_{22} & ... & b_{2n} \\ \vdots & \vdots & \ddots & \vdots \\b_{m1} & b_{m2} & ... & b_{mn}\end{bmatrix}\)
   
   Hadamard Product between Matrix \(A\) and Matrix \(B\) is calculated by Multiplying the Corresponding Elements of Matrix \(A\) and Matrix \(B\) as given in following
   
   \(A \circ B=B \circ A=\begin{bmatrix} a_{11} & a_{12} & ... & a_{1n}\\ a_{21} & a_{22} & ... & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\a_{m1} & a_{m2} & ... & a_{mn}\end{bmatrix}\circ \begin{bmatrix} b_{11} & b_{12} & ... & b_{1n}\\ b_{21} & b_{22} & ... & b_{2n} \\ \vdots & \vdots & \ddots & \vdots \\b_{m1} & b_{m2} & ... & b_{mn}\end{bmatrix}= \begin{bmatrix} a_{11}\circ b_{11} & a_{12}\circ b_{12} & ... & a_{1n}\circ b_{1n}\\ a_{21}\circ b_{21} & a_{22}\circ b_{22} & ... & a_{2n}\circ b_{2n} \\ \vdots & \vdots & \ddots & \vdots \\a_{m1}\circ b_{m1} & a_{m2}\circ b_{m2} & ... & a_{mn}\circ b_{mn}\end{bmatrix}\)
3. Follwing are some examples of Hadamard Product of Matrices.
   
   \(\begin{bmatrix} 2 & 9 & 1\\ 3 & 1 & 2\end{bmatrix} \circ \begin{bmatrix} -3 & 7 & 2 \\ 6 & -5 & 3\end{bmatrix} = \begin{bmatrix} 2 \circ -3 & 9 \circ 7 & 1 \circ 2\\ 3 \circ 6 & 1 \circ -5 & 2 \circ 3\end{bmatrix} = \begin{bmatrix} -6 & 63 & 2\\ 18 & -5 & 6\end{bmatrix}\)
   
   \(\begin{bmatrix} 7 & 2 \\ -6 & 5 \\ 4 & -3 \end{bmatrix} \circ \begin{bmatrix} -2 & 9 \\ 3 & -13 \\ 11 & 1 \end{bmatrix} = \begin{bmatrix} 7 \circ -2 & 2 \circ 9\\ -6 \circ 3 & 5 \circ -13\\ 4 \circ 11 & -3 \circ 1 \end{bmatrix} = \begin{bmatrix} -14 & 18\\ -18 & -65\\ 44 & -3 \end{bmatrix}\)
   
   
4. You can use the Matrix Hadamard Product / Double Dot Product Calculator to calculate Hadamard Product of Matrices.